How do you solve #|(3x - 5) / 6| > 4#?

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Answer 1 · 2017-02-16T08:24:27

The solutions are #x in ]-oo,-19/3[uu]29/3,+oo[#

Let 's rewrite the inequality

#|(3x-5)/6|>4#

#|1/2x-5/6|>4#

There are 2 solutions

#color(red)(solution 1)#

#1/2x-5/6>4#

#1/2x>4+5/6#

#1/2x>29/6#

#x>29/3#

#color(red)(solution 2)#

#-1/2x+5/6>4#

#1/2x<5/6-4#

#1/2x<-19/6#

#x<-19/3#

Putting it all together

#x in ]-oo,-19/3[uu]29/3,+oo[#